Question

Proofs whole page for 50 points ( serious answers only or report and 1 star )

Answer 1

Question 1:

1) Given - It is given in the problem

2) Corresponding Angles Postulate - If a transversal (line l) intersects two parallel lines (line h and line g), then the corresponding angles must be equal.

3) Transitive Property of Congruence - Since it's given that
`\angle1\cong\angle5` and we showed in line 2 that
`\angle1\cong\angle2`, it should be true that
`\angle2\cong\angle5`

4) Converse of Corresponding Angles Postulate - If a transversal (line g) intersects two lines (lines l and m), and the corresponding angles that form have equal measure, then the lines are parallel.

Question 2:

1) Given - It is given in the problem

2) Definition of Angle Bisector - It's given that
`\overline{DC}` bisects
`\angle BDE`, which means that
`\overline{DC}` is the angle bisector, and the angle is divided into two angles of the same measure.

3) Transitive Property of Congruence - Since we showed in line 2 that
`\angle1\cong\angle2` and its given that
`\angle2\cong\angle3`, it should be true that
`\angle1\cong\angle3`

4) Converse of the Alternate Interior Angles Theorem - If a transversal (
`\overline{BD}`) intersects two lines (
`\overline{AB}` and
`\overline{CD}`) and the alternate interior angles formed have the same measure, then the lines are parallel.